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This lecture on Convex Optimization by the instructor covers course organization, recommended books, mathematical optimization problems, global minimizers, local minimizers, E-optimal solutions, solution concepts, optimization methods, efficient numerical methods, inefficient numerical methods, purpose of the course, main take-away points, course outline, lines, affine, convex, and conic sets, affine, convex, and conic combinations, affine, convex, and conic hulls, and their elementary results.